Distributed power architecture is now commonplace — with benefits that include enhanced circuit layout, design flexibility, and improved reliability through the elimination of a single point of failure. This, in turn, has fueled the rapid market growth for off-the-shelf dc-dc converters. Because dc-dc converters are, by nature, a source of heat, engineers tasked with specifying an off-the-shelf dc-dc converter solution must carefully consider the thermal management implications of their selection.

Compact and efficient quarter-brick dc-dc converters with industry-standard dimensions of 2.3 in. × 1.5 in. × 0.5 in. (58.4 mm × 38.1 mm × 12.7 mm) are a popular choice for engineers developing rack-mounted DPA applications in the data communications and telecommunications arena. These devices are replacing more conventional half-brick products in space-limited applications that have high power requirements. Single- and dual-output quarter brick devices are available with power ratings over 100W and with typical input voltages ranging from 12Vdc to 75Vdc. Output voltages are between 12V and below 1V, depending on the converter chosen. Generally, these devices offer isolation between input and outputs and incorporate features designed to provide protection against conditions such as input undervoltage, input overvoltage, output overvoltage, short circuits, and overtemperature. In addition, many quarter brick dc-dc converters offer other functions that minimize the need for additional circuitry, such as remote on/off control and output voltage trim.

Efficiency ratings for isolated quarter brick dc-dc converters are in the 85% range or better. For example, C&D Technologies' VSX75 dual-output 75W converter is a quarter-brick unit with a 1500Vdc input-to-output isolation that employs a proprietary high-power density technology to achieve a 90% efficiency rating (**photo**). However, no matter how efficient a dc-dc converter is, some power will always dissipate as heat to the surroundings. This heat is one of the main factors in both calculated and demonstrated mean-time-to-failure (MTTF) and can ultimately affect the overall system reliability.

Therefore, an engineer designing a DPA system must carefully consider the subject of thermal management.

### Thermal Management

The efficiency (η) of a dc-dc converter is the ratio of output power to input power (P_{OUT}/P_{IN}), while power dissipated as heat (P_{diss}) is P_{IN} - P_{OUT} and, therefore:

P_{diss} = P_{OUT}/η- P_{OUT} = [(1-η)/η)] × P_{OUT} (1)

Equation (1) states that dissipated power is a function of efficiency, which is dependent on the percentage of rated output power provided to the load (**Fig. 1, on page 15**). Other variables affecting efficiency are the system's operating (ambient) temperature (T_{a}) and the source voltage.

When it comes to thermal management solutions for quarter-brick dc-dc converter designs, you must consider several factors. Generally, the starting point is the baseplate, which is the primary heat dissipation path from the converter. For example, the VSX75 converter operates with a -40°C to 100°C baseplate temperature. If the baseplate temperature exceeds this, an overtemperature protection (OTP) circuit shuts the converter down to prevent damage. And although the unit restarts itself when the temperature drops back below 100°C, a well-designed application ensures that the baseplate temperature never reaches these levels and that no unexpected shutdowns occur. This means the designer's goal must be to transfer as much heat from the baseplate into the surrounding environment as efficiently and inexpensively as possible.

Three basic methods of providing heat transfer are radiation (heat transfer between objects at different temperatures), conduction (heat transfer through a solid medium), and convection (heat transfer through air or fluid). Convection is the primary heat transfer mechanism in most applications, although all three are usually present to some degree and therefore contribute to the development of an effective cooling system. Let's examine each of these heat-related functions.

Radiation is present in almost all power systems, regardless of the ultimate cooling scheme. Key factors affecting heat dissipation through radiation include the converter's temperature and position relative to other parts in the system as well as spacing and surface finish of the parts in question. Components such as power transistors and rectifiers, for example, may reach a higher temperature than the converter and lower its performance as a result of heat absorption. However, in most cases the converter is likely to be at a higher temperature than its surroundings and, as a result, will radiate rather than absorb heat — although the overall contribution to heat transfer may be relatively small. Because of this, it's often best to neglect radiant heat transfer and simply be aware that its presence provides a small safety margin beyond the calculated limits.

In most cases, heat conduction occurs between the converter baseplate and an attached heatsink or other heat-conducting material. The baseplate temperature rise, as illustrated in Fig. 2, is:

T_{b} = T_{S} + (θ_{bs} × P_{diss}) (2)

Where:

T_{b} = Baseplate temperature

T_{S} = Conducting material temperature

θ_{bs} = Thermal resistance

P_{diss} = Power dissipated within the converter

As the equation shows, minimizing θ_{bs} minimizes the total temperature rise. You can accomplish this by maximizing the junction surface area and the surface flatness of the heat-conducting material. Because of random surface irregularities present in most materials, a thermally compliant material should be used to join the two surfaces. In fact, with proper care and planning, junction thermal resistance should be reduced to less than 0.1°C/W.

Convection is the most popular method of cooling. Convection cooling schemes fall into free and forced convection solutions. Free convection refers to heat transfer into cooler, still air and is thus the simplest scheme to implement and the most reliable because it requires no moving parts. On the downside, free convection typically requires a larger heatsink — a problem in space-limited applications. Although forced convection provides significantly increased levels of cooling, it presents some design challenges. First, the chosen fan must be correctly matched with the heatsink to provide the desired surface-to-air thermal resistance. Furthermore, fan operating life is an important criterion if the system is to work reliably throughout its lifetime. Finally, airflow channeling and filtering may be needed for optimal cooling.

### Baseplate Temperature

To determine if a heatsink or additional airflow (or both) is required, you must calculate the converter's baseplate (i.e., case) temperature under the worst-case conditions. This requires Equation (1) and the following equations:

Temperature rise = (P_{diss} × θ_{ba}) = P_{OUT} × θ_{ba} [(1- η)/ η] (3)

Where:

θ_{ba} = Thermal resistance from base to ambient Maximum output power = [T_{Base}(max) - T_{a}] / [θ_{ba} {(1- η)/η}] (4)

Where:

T_{Base}(max) = Maximum baseplate temperature

T_{a} = Ambient temperature

Maximum thermal impedance = [T_{Base}(max) - T_{a}] / [P_{OUT} {(1- η)/η}] (5)

We can see how these equations can be used by considering the example of the VSX60 60W, quarter-brick, dual-output dc-dc converter used to drive a load of 53W in a cabinet at 50°C with an airflow of 200 LFM (linear feet per minute). The input voltage is typically 48V but may rise to 52V under some conditions. Distributed load current is 4A for the 5V output and 10A for the 3.3V output. It's necessary to first ascertain the heat generated by considering the converter efficiency, which is:

Efficiency (η) = η_{pds} × η_{vIN} × η_{tld} × η_{ldd} (6)

Where:

η_{pds} = Minimum efficiency of the converter (from its data sheet)

η_{vIN} = Efficiency adjustment factor based on a graph of normalized efficiency vs. input voltage

η_{tld} = Efficiency adjustment factor based on a graph of normalized efficiency vs. output load

η_{ldd} = Efficiency adjustment factor based on a graph of normalized efficiency vs. load distribution.

These graphs are available from most manufacturers. From this data, the efficiency calculation for the VSX60 is: Efficiency (η) = 0.89 × 0.997 × 1.00 × 0.996 = 88.38%.

Because efficiency is P_{OUT}/P_{IN}×100%, the dissipated power P_{diss} can be calculated: P_{diss} = [(1-η)/η] × P_{OUT} = [(1-0.8838)/0.8838]×53 = 6.968W.

The temperature rise of the baseplate can then be determined by multiplying θ_{ba} (from the thermal impedance chart in Table 1) by the dissipated power: Temperature rise (T_{R}) = (P_{diss} × θ_{ba}) = P_{OUT} × θ_{ba} [(1- η)/ η] = 6.968 × 7.49 = 52.19

Once the temperature rise of the baseplate is known, the worst-case temperature of the plate is determined by adding the ambient temperature: Baseplate temperature (T_{BP}) = T_{R} + T_{A} = 52.19 + 50 = 102.19°C.

As the VSX60 converter is rated for operation with baseplate temperatures up to 100°C, this calculation has identified that it's outside its specified range. Some ways to solve this problem include reducing the output power or lowering the maximum ambient temperature. Alternatively, it may be possible to reduce the thermal resistance from baseplate to ambient through additional forced-air cooling and/or the addition of a heatsink.

You can use the following equations to calculate maximum output power that can be delivered or the maximum thermal resistance that the converter will tolerate. Then use the maximum thermal resistance in conjunction with the thermal impedance chart in Table 1 to determine the correct combination of airflow and heatsink.

In the example above, the maximum output power would have to be reduced using the equation:

Maximum output power = [T_{Base}(max) - T_{a}] / [θ_{ba} {(1- η)/η}] (7)

Usi ng a baseplate temperature of 95∞C to ensure a suitable safety margin:

Maximum output power = (95-50)/[7.49 ×{(1-0.8838/0.8838}] = 45.6W.

If the thermal impedance can be changed, then the equation:

Maximum thermal impedance = {T_{Base}(max) - T_{a}] / P_{OUT} [(1- η)/η] (8)

Maximum thermal impedance = (95-50)/[53 × {(1-0.8838/0.8838)}] = 6.458°C/W.

As seen in the thermal impedance chart in **Table 1**, this example requires 400 LFM of airflow with no heatsink. Alternatively, **Table 2** shows that using just 200 LFM of airflow is required if the converter's dedicated heatsink is also used. A fan that delivers at least this airflow is thus required. Typically, fan manufacturers provide data in airflow (CFM) vs. pressure drop, where CFM = LFM×air cross-sectional area.

### Open-Frame DC-DC Converters

Situations will arise when space constraints or layout restrictions mean that it's not possible or convenient to add a heatsink to a dc-dc converter. In the majority of cases, this means that forced air becomes the only viable thermal management solution for cooling the converter and ensuring that the case temperature remains within the specified operating limits. In such situations, consider using one of the growing number of open-frame dc-dc converters now available. The VSX converter series of 40W, 50W, 60W, and 75W quarter-brick devices, for instance, features unencapsulated options at each power level. These devices offer exactly the same specifications as their encapsulated counterparts, with the exception of airflow requirements and unit weight.

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